Event-based state-space model predictive control of a renewable hydrogen-based microgrid for office power demand profiles

Event-based State-Space Model Predictive Control of a renewable hydrogen-based microgrid for office power demand profiles? M. Castillaa,∗ , C. Bordonsb, A. Visiolic aCentro Mixto CIESOL, ceiA3, Universidad de Almer´ıa. Ctra. Sacramento s/n. 04120, Almer´ıa, Spain bUniversidad de Sevilla. Camino de los Descubrimientos, s/n. 41092, Seville, Spain cUniversity of Brescia. via Branze 38. 25123, Brescia, Italy Abstract This paper focuses on the design and implementation of an event-based control architecture to manage a renewable-based microgrid. This microgrid has renewable-energy generation and a hybrid energy storage system that uses electricity and hydrogen. The main load of the microgrid is the energy demand of an office. The primary control objective is to satisfy the load demand using the available renewable generation and stored energy while reducing the amount of energy purchased from the Utility Power Grid (UPG). To do that, the control architecture, which has been defined within an event framework, makes use of a set of state-space model predictive controllers which are selected as a function of a variable sampling period. To evaluate the performance of the proposed control architecture, simulation tests for a typical day of summer as well as an analytical study is performed. Furthermore, a comparison of the obtained results with a classic state-space model predictive control approach is also included. The obtained results show that the use of the event-based control architecture allows a significant reduction of the number of changes in the control action at ?This work has been funded by the research project CONFIGURA (DPI2016- 78338-R) from the Spanish Ministry of Economy and Competitiveness and AGERAR (0076 AGERAR 6E) founded by the European Commission. ∗Corresponding author Email addresses: [email protected] (M. Castilla), [email protected] (C. Bordons), [email protected] (A. Visioli) Preprint submitted to Journal of Power Sources October 9, 2019 the expense of an acceptable deterioration of set-point tracking for a microgrid with several types of electrochemical storage. Keywords: Event-based control, Model Predictive Control, microgrids, thermal comfort, energy efficiency, co-simulation 1. Introduction These days, a transition from centralized and fossil-fuels based energy systems to distributed renewable-energy based ones is taking place mainly due to the fact that non-renewable energy sources are more and more exhausted [1]. Hence, it is necessary to develop new control algorithms able to manage the effects related to the intermittence and distribution of energy, as well as new demand profiles. For this reason, the use of microgrids has spread in recent years. A microgrid can be defined as a group of generators, loads and energy storage systems that can be managed in both connected to grid or islanded operating modes with the principal aim of providing electricity in a reliable way [2]. In that way, a microgrid can be used to guarantee Quality of Service for local loads just as hospitals, shopping centers, office buildings, etc. Nevertheless, as it is pointed out in [3], the development of microgrid control algorithms is a difficult task which presents several problems and important challenges. Specifically, [3] focuses on optimal management of microgrids. Moreover, it is possible to find in literature many other works related to energy management of a microgrid which make use of different approaches, such as, heuristic algorithms [4], stochastic control [5, 6], neural-network and fuzzy logic techniques [7]. Besides, Model Predictive Control (MPC) is one of the most used techniques since it allows the integration of both generation and load predictions and energy price estimations. For instance, in [8] optimal controllers for distributed renewable generation networks and batteries storage are presented. Likewise [9, 10] illustrates the use of centralized MPC techniques. In [11] a review of different types of control approaches applied to microgrids (such as rule-based, model predictive control and occupancy based model predictive 2 control for buildings) is performed. On the other hand, the use of event-based control approaches presents several advantages, such as the computation of new control signals only when an event is detected or the reduction in the use of resources [12]. Besides, these approaches are very beneficial when they are applied to distributed systems, since they can decrease the information exchange among the elements which compose the system [13]. For these reasons, in the last years the use of eventbased techniques has spread widely and they have been applied to a huge variety of systems. For example, to control Heating, Ventilation and Air-Conditioning (HVAC) systems in buildings [14, 6], distributed solar collector fields [15], pH level in photobioreactors [16], etc. However, up to our knowledge, there are not many works which have applied event-based control to manage a microgrid. Sometimes it is required to consider specific variables like the connection status (connected/disconnected) or changes in the behaviour of the equipment during the normal operation (for example different charging/discharging efficiency coefficients for a batteries bank) within the control problem. For this reason, it is necessary to develop and analyse new configuration, modelling and control techniques. Therefore, the main objective of this paper is the development of a control approach within the framework of hybrid MPC which allows the efficient management of a renewable-energy based microgrid with two types of electrochemical storage: batteries and hydrogen (fuel cell and electrolyzer). Moreover, the developed strategy has considered some deterioration of storage systems criteria to provide a larger durability. To do that, the use of eventbased MPC control is ideal since it maintains all the individual advantages of both MPC and sampling techniques based on events. In more detail, these characteristics of an event-based MPC have been used to establish a trade-off between the performance of the control system (accuracy) and the necessary effort (resources used by the control strategy). In this way, event-based control systems can reduce the use of resources (by the application of new control signals only if it is required), and thus, also the economical costs at the expense of an insignificant deterioration of the control system performance. 3 A control approach has been developed in order to manage an existing laboratory-scale renewable-energy based microgrid located at the University of Seville [17]. The power supported by this microgrid is similar to the one demanded by an office room, see Table 1. The principal goals of the proposed control system, from a performance point of view, are to satisfy realistic load profiles for an office-building, to maintain the energy storage levels within established security limit and to minimize the amount of energy exchanged with the Utility Power Grid (UPG). Additionally, the degradation of the storage devices (battery, electrolyzer and fuel cell) is taken into account; as analysed in [18], this is closely related to the changes in the control actions, so a control strategy that avoids frequent and sudden changes in the use of storage devices can improve their lifetime. More in detail, it has been supposed that the microgrid should satisfy the energy demanded by an office-room considering its thermal comfort specifications and the physical constraints of the microgrid itself. Hence, a building has been simulated and controlled by means of co-simulation techniques and the total energy amount demanded by a room of this building has been quantified taking into account not only the energy demanded by the HVAC system but also, the energy demanded by artificial lighting and electrical appliances. Henceforth, to manage the renewable-energy based microgrid, an event-based state-space MPC control has been designed and implemented. In this case, two different types of events have been defined: threshold and time-based events. The effectiveness of the proposed control architecture has been analysed by means of several simulation tests for a typical summer day in Seville. In addition, the obtained results have been compared with a classic state-space MPC approach. The obtained results are promising since they demonstrate that it is possible to reduce the number of actuations around a 65%, at the expense of an acceptable deterioration of the performance and an increment of the energy exchanged with the UPG less than 1.35 kW h for a whole day of operation for the selected solution. Further, even if less important in this application, the computing time is reduced up to 70%. The structure of the rest of the paper is organized as follows: Section 2 4 describes the methodology used to obtain realistic energy demand profiles for an office-room considering thermal comfort constraints. Section 3, describes the renewable-energy microgrid. Section 4 performs a detailed explanation of the event-based state-space control architecture presented in this paper. Section 5 introduces the optimization procedure followed to select the main parameters of the event-based strategy. Section 6 presents the simulation results obtained for a typical summer day in Seville. Finally, Section 7 summarises main conclusions and future works. 2. Energy demand: Thermal comfort control of an office-room In this paper, it has been supposed that the renewable-energy based microgrid is used to satisfy the energy demanded by an office-room. Therefore, obtaining realistic energy consumption profiles is a cornerstone, and thus, it is necessary to determine the energy required by its users in order to develop their daily activities, taking into consideration thermal comfort constraints. Besides, for the purpose of assuring a comfortable situation for the users of a room from a thermal point of view, the use of adequate control systems is required [19]. Moreover, to design and implement appropriate control strategies, it is fundamental to have a building model able to capture its dynamic behaviour. In this paper, an office building and a room-level thermal comfort controller have been simulated by means of co-simulation techniques. Co-simulation can be defined as the integration of various simulation tools at run-time coupling [20, 21]. More specifically, the EnergyPlus engine [22] has been used to simulate the dynamic behaviour of the building whereas the thermal comfort controller has been designed using Matlab. Furthermore, it is required to establish a communication at simulation time between EnergyPlus and Matlab, and thus, the Building Control Virtual TestBed (BCVTB) tool has been utilised [23]. In more detail, one of the buildings which have been included as an example of how to use BCVTB tool has been selected and modified in order to be considered as an office building. It occupies an estimated total surface equal to 310 m2 5 and comprises two floors and a basement. At each floor, two thermal zones which face South and North have been considered, see figure 1(a). However, to evaluate the performance of the event-based state-space MPC architecture presented in this paper, the south zone of the first floor (ZSF1) has been selected as a characteristic office-room due to the dimensions of the renewable-energy based microgrid. Furthermore, the following assumptions have been considered in order to simulate the building: •The maximum occupation rate of the selected room has been established to 10 people. Moreover, it has been fixed that the first five workers arrive at 7 a.m. Afterwards, at 8 a.m. three more workers arrive to their workplace. The occupation rate of the room is fixed to its maximum value from 10 a.m. to 1 p.m. and from 3 p.m. to 5 p.m. From 1 p.m. to 3 p.m. and from 5 p.m. to 6 p.m. the occupation rate has been established to five people. Finally, the last two workers abandon the room at 7 p.m., see 1(b). •The building is located in the city of Seville. So, hourly weather data for Seville obtained from [22] has been used. This dataset contains International Weather for Energy Calculations (IWEC) data originated based on almost 20 years of data originally archived at the U.S. National Climatic Data Centre and supplemented by solar radiation calculated as a function of earth-sun geometry and cloud amount information [24]. As an example, main outdoor environmental variables for a typical summer day can be observed in figure 1(c). •The HVAC systems are operated from 6 a.m. to 7 p.m.. As it can be observed in figure 1(c), Seville has hot summers with a maximum mean outdoor temperature approximately equal to 36oC. Therefore, to reach a comfortable thermal sensation inside buildings the use of active strategies such as HVAC systems, able to control indoor climate, is required. At this point, it is important to mention that EnergyPlus allows the control of the 6 a) Simulated office building: 3D overview b) Profile of people inside the room c) Outdoor conditions for summer in Seville Figure 1: Principal characteristics of the building simulated with EnergyPlus 7 indoor environment through zone level control algorithms by modifying, in an appropriate way, the set-points defined for these zones. Those algorithms can be defined as a function of a thermostat, of the operative temperature or the Predicted Mean Vote (PMV) index [25]. Therefore, the designed control algorithm in Matlab should estimate the adequate set-points based on the selected zone control algorithm, that is, indoor air temperature, operative temperature or PMV index, respectively. In this paper, a zone control based on the PMV index has been performed. This index allows the prediction of the mean response about thermal sensation of a large group of people exposed to particular thermal conditions for a certain amount of time. Concretely, the steps that have been followed to develop a thermal comfort controller for an office-room using co-simulation techniques can be summarized as follows: •An office building has been configured and simulated in EnergyPlus. It will be considered as a room simulator from thermal comfort control point of view. •A characteristic room has been selected (ZSF 1) and a model of it has been obtained by means of classical identification techniques [26]. To do that, a Pseudo-Random Binary Signal (PRBS) has been designed in Matlab and it has been applied to the EnergyPlus building model using BCVTB tool. The main goal was to capture enough data of the selected room to allow the identification of a model of the room. •Afterwards, a simple control signal has been designed and implemented in Matlab in order to maintain the PMV index within the limits established by international standards. To do that, the model identified beforehand has been used. Moreover, it should be taken into consideration that this controller is subject to several disturbances such as outdoor air temperature and room occupation. Simulation results of the thermal comfort controller can be observed in figure 2. •Finally, once that the room simulator (office building model developed in 8 EnergyPlus) and the thermal comfort controller (Matlab) have been designed and implemented, a control architecture which allows the thermal comfort sensation to be maintained into the selected room has been implemented using co-simulation techniques. To do that, EnergyPlus and Matlab will simulate the building and the thermal comfort controller respectively. Moreover, they will exchange the necessary information for a correct operation using BCVTB interface at run-time coupling. Figure 2: Results of the thermal comfort controller within the selected room A more detailed description of the methodology followed to identify the room model and to implement the thermal comfort control system has not been included, since it is out of the scope of the work presented in this paper. Several works and results related to this topic can be found in [19]. Finally, the energy demanded by this room to satisfy users’ necessities related to their quotidian activities and thermal comfort has been obtained from EnergyPlus simulation engine. Specifically, the energy consumed by artificial lighting and electrical appliances has been considered and moreover, the energy used by the HVAC system to maintain a thermal comfort sensation has also been taken into consideration. These energy demands have been configured to depend on the number of people and the type of lights and electrical appliances inside the room. Therefore, it has been supposed that there is a computer with similar characteristics for each person. Data related to lighting and electrical 9 case, it looks for two types of events: time events and threshold ones. Afterwards, the occurrence of an event and the exact time instant it has happened are sent to the controller unit. •Controller unit: This unit is composed of a set of state-space MPC (SSMPC) controllers and an event classification sub-unit. Moreover, it is responsible for obtaining new control signals (PH2and Pgrid) when an event is detected. Concretely, the event classification module analyses the received event and selects the most appropriate SSMPC controller as a function of time in which the new event is detected. Afterwards, the selected SSMPC controller recalculates control signals by solving the MPC problem defined in Section 4.3. Figure 5: Event-based state-space MPC control architecture. In order to operate correctly the event-based state-space MPC control strategy, it is necessary to define some concepts and constraints related to different sampling times and the occurrence of events: •The outputs of the controlled process, that is, SOC and LOH are provided by the microgrid simulator. These variables are measured by means of a 16 Sensor module and sampled through a constant sample time denoted as Tbase. •Afterwards, the event-logic module analyses at each Tbase time instant the process outputs in order to identify the occurrence of a new event. Specifically, two types of events have been defined: threshold based ones, which make use of a parameter denoted β; and time-based events, that depend on Tmax. More information about the event-logic module can be found in Section 4.2. •Finally, control signals (PH2,Pgrid) are calculated and applied to the microgrid as a function of a variable sampling period Tf, which depends on the occurrence of an event. Tfmust be a multiple of Tbase and below a maximum sampling period Tmax =nmax ·Tbase. The selection of Tmax is an important cornerstone in this type of controllers since it will influence their performance. Hence, it is necessary to define a set of state-space MPC controllers based on the variable sampling period Tf. This group of controllers makes use of the state-space model given by (6) discretized with different sampling periods (Tf∈ {Tbase,2·Tbase,...Tmax}). In the following subsections, a detailed explanation of the main elements which compose the proposed control architecture has been included. 4.2. Event-logic module In an event-based controller, control signals are not estimated in a synchronous mode, but are calculated when a new event is detected. Therefore, the sampling period of the controlled system is regulated by the event-logic module. More specifically, it is responsible for verifying some conditions over the process in order to detect possible events, and whenever necessary, to update the sampling period of the controlled system and the state-space MPC controller used. As discussed before, in this paper two types of conditions have been defined as events. Hence, when one of those conditions is detected, the event-logic 17 module generates a new event which is transmitted to the controller unit together with the main process variables necessary to generate a new set of control signals. In particular, the first condition is associated with a threshold event applied to the outputs of the controlled process. In other words, a new event is generated when the existing difference between one of the outputs of the process (SOC or LOH) and their associated set-point values is greater than a fixed tolerance β, see (7). This type of conditions is known as level crossing sampling technique [31], and it can be formally expressed as, |w(t)−y(t)|> β (7) where the output of the system y(t) coincides with the state x(t), that is, y(t) = x(t)=[SOC(t); LOH(t)]. On the contrary, the second condition is related to a time event which is used for stability and performance improvement. Specifically, this condition generates a new event when the time between two consecutive events is greater that a maximum established time, that is, Tmax, see (8). Formally, it is t−tei≥Tmax (8) where, tis the current time-instant and teirepresents the time-instant in which the last event was detected. Therefore, to detect a new event, at each period Tbase the previous mentioned conditions are checked, and this will originate a variable sampling period denoted as Tf. As it can be inferred from (7) and (8), the selection of βand Tmax is a critical issue which should be addressed in an appropriate way. 4.3. State-Space Model Predictive Control As it was discussed previously, the controller unit within the event-based control architecture is composed of a set of state-space MPC controllers. In this section, the design of a classic state-space MPC controller which has been 18 discretized using a certain sample time Tfis explained. MPC is distinguished by the explicit use of a model of the controlled system in order to predict its state along a prediction horizon Np[32]. Specifically, every Tftime period, a sequence of control signals {u(t),· · · , u (t+Np−1)}is obtained by optimizing a cost function, see (9). Then, the first component of this sequence is applied to the microgrid at time instant twhile the others are dismissed. Subsequently, the complete procedure is performed again at next sampling time (t+ 1) using more updated information. The cost function is expressed as J(Np, Nu) = Np−1 X j=1 [ˆx(t+j|t)−xref (t+j)]Tδ[ˆx(t+j|t)−xref (t+j)] + Nu−1 X j=1 [∆u(t+j|t)]Tλ[∆u(t+j|t)] + Nu−1 X j=1 [u(t+j|t)]Tγ[u(t+j|t)] (9) where, ˆx(t+j|t) represents an optimal jstep-ahead prediction of the system output estimated at sampling time t+jwith the information available at sampling time t,Npand Nuare the prediction and control horizons, respectively, and δ,λand γare weighting matrices used to balance the set-point tracking, the control increment and the control effort, respectively. Finally, xref (t+j) is the desired set-point for the states. Besides, it is worthwhile to mention that it has been considered that all the signals have a sampling period Tf(t=kTf, k = 1,· · · ,∞). In this paper, these values have been established as δ= [0.01 0; 0 0.01], λ= [50 0; 0 1000] and γ= [10 0; 0 300]. These values have been selected to provide a higher priority to the use of the battery bank over the hydrogen path and, moreover, to reduce the exchange of energy with the UPG. Besides, set-point tracking weighting matrix, δ, has been chosen not to guarantee a perfect set-point tracking but to maintain SOC and LOH within an established security limits that allow the reduction of the number of events, and thus, the number of actuations. Furthermore, the prediction 19 and control horizons have been established to Np= 5 and Nu= 2, respectively. Finally, the references values for SOC and LOH have been established to xref = [60% 45%]T, respectively since it has been considered to be the nominal operating point because it represents a compromise between operation flexibility and guaranteed operation autonomy. For this reason, the model used within the SSMPC has been linearized around this operation point. In addition, at this point it is necessary to highlight that, although it is possible to find in literature other works which do not consider set-point tracking within storage systems [33, 34], in this paper it has been decided to include it as a not very representative term of the cost function with the purpose of not depleting storage systems. Therefore, the state-space MPC controller is responsible for estimating the future control signals sequence by minimizing the cost function given by (9). To do that, it is required to obtain the optimal prediction of x(t+j) for j∈ {0,1,· · · , Np−1}using the state-space model of the microgrid, see (6). The following assumptions have been considered in order to calculate the optimal prediction of x(t+j). Firstly, the state-space model given by (6) has been rewritten according to (10) where Aand Care identity matrices of an appropriate size. x(t+ 1) = Ax (t) + Bu (t) + Eω (t) y(t) = Cx (t) (10) As it was commented in Section 3, the system is subject to a state disturbance, ω(t) = Pnet, and thus, it is necessary to deal with it in an adequate way. To do that, the overall process model has been augmented to include the disturbance, following the formulation proposed by [35]. Although it would be ideal to include the disturbance forecast within the control problem, as it is not available, the disturbance has been considered constant over the entire prediction horizon, so that the augmented model results in 20 ˜x(t+ 1) = Ad˜x(t) + Bdu(t) y(t) = Cd˜x(t) where, ˜x(t+ 1) =   x(t+ 1) ω(t+ 1)  ;Ad=  A E 0I  ; Bd=  B 0  ;Cd=hC0i(11) Secondly, the state-space controller has been implemented using an incremental formulation of the state space model, that is, considering the control increment ∆u(t) instead of the control signal u(t), where ∆u(t) = u(t)− u(t−1) [32]. Hence, defining a new state which depends of the previous augmented one xf= [˜x(t)u(t−1)]T= [x(t)ω(t)u(t−1)]T, the incremental model takes the general form given by xf(t+ 1) = Mxf(t) + N∆u(t) y(t) = Qxf(t) where, M=  AdBd 0I  ;N=  Bd I  ;Q=hCd0i(12) that is, M=            100.0936 0.0936 0.0936 0 1 0 −0.3397 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1            ;N=            0.0936 0.0936 −0.3397 0 0 0 1 0 0 1            ; 21 Q=  10000 01000  (13) Therefore, taking into consideration the issues mentioned above, the output of the model for sample time t+j, assuming that the value of states and future control increments are known, can be estimated recursively as y(t+j) = QMjxf(t) + N−1 X i=0 QMN−i−1N∆u(t+i) (14) In addition, this equation can be expressed in vectorial form just as: y= Fˆx(t) + H∆u, where F=QM QM2· · · QMNpT;Hrepresents a block lower triangular matrix with its non-zero elements equal to Hij =QMi−jN and ∆u = [∆u(t) ∆u(t+ 1) · · · ∆u(t+Np−1)]Tsymbolises a sequence of future control increments. Hence, it can be also inferred that the output of the system depends on its current state and on a sequence of future control increments, which is the decision variable that have to be estimated. The sequence of control increments ∆u is obtained by minimizing the cost function given by (9). Moreover, considering the recursive procedure to estimate the process output in its vectorial form, the cost function equation can be rewritten as: J(Np, Nu)=(H∆u +Fˆx(t)−xref )Tδ(H∆u +Fˆx(t)−xref ) +∆uTλ∆u +uTγu(15) Finally, if the system is not subject to any constraint, it is possible to obtain an analytical solution from the previous equation. Nevertheless, in this case several constraints have been defined, and thus, a quadratic programming problem should be solved using the previously defined quadratic cost function with linear inequality and equality constraints [32]. In particular, several hard constraints have been included to ensure an adequate performance of the microgrid. In other words, they act as physical limitations of the connection for 22 the grid operation and the hydrogen path by applying limitations to the control inputs variables and their increments: −0.9kW ≤PH2(t)≤0.9kW (16) −2.5kW ≤Pgrid (t)≤2.5kW (17) −0.9kW s-1 ≤∆PH2(t)≤0.9kW s-1 (18) −2.5kW s-1 ≤∆Pgrid (t)≤2.5kW s-1 (19) Furthermore, several constraints concerning the state variables, SOC and LOH, have been included with the main purpose of physically limiting the batteries bank and the level of hydrogen within the storage tank: 40% ≤SOC ≤90% (20) 10% ≤LOH ≤90% (21) Besides, it is worth emphasizing that the power of the batteries bank can be obtained from (3). Finally, The State-Space Model Predictive Control is summarized in Algorithm 1. 5. Optimal selection of Tmax and βparameters As it was commented before, the choice of Tmax and βis a critical issue since it influences the performance of the obtained results. The main goal of the eventbased control architecture presented in this paper is to reduce the number of actuations without deteriorating too much the system’s performance. Hence, it is a multiobjetive optimization problem. A multiobjective optimization problem can be defined as the search for a vector of decision variables able to satisfy certain constraints and, at the same time, to optimize a vector of objective functions [36]. Therefore, a multiobjective problem is characterized by having two or more competing objectives (in conflict) which should be simultaneously minimized (or maximized) satisfying 23 Algorithm 1 State-Space MPC problem Define the simulation time and current simulation time: tsim and k= 0. Define the initial conditions of manipulated inputs, outputs and disturbances. while k≤tsim do 1. Measure the current states (x), manipulated inputs (u), outputs (y) and disturbances (ω). 2. Determine a new set of control signals along the control horizon, u= [u(k|k), u (k+i|k), ..., u (k+Nu−1|k)], by solving the quadratic problem defined by: min J(Np, Nu) = Np−1 X j=0 δ[ˆx(k+j|k)−xref (k+j)]2 + Nu−1 X j=0 λ[∆u(k+j|k)]2+ Nu−1 X j=0 γ[u(k+j|k)]2 s.t. x(k+ 1) = Ax (k) + Bu (k) + Eω (k) Pdem (k) = PH2(k) + Pbat (k) + Pgrid (k) + Pren (k) −0.9kW ≤PH2(k+j)≤0.9kW −2.5kW ≤Pgrid (k+j)≤2.5kW −0.9kW s-1 ≤∆PH2(k+j)≤0.9kW s-1 −2.5kW s-1 ≤∆Pgrid (k+j)≤2.5kW s-1 ∀j= 0 . . . Nu−1 3. The control signal u(k|k) is applied to the process whilst the other control signals calculated in the previous step are discarded. 4. k = k + 1; end while 24 several constraints [37]. The solution to this type of problems is not unique. In other words, it is not feasible to find an ideal solution able to optimize all the objective functions. Nevertheless, there is a possibility of determining a set of non-dominated solutions known as optimal solutions [37] which satisfy some selected criteria. More specifically, this choice is performed by using some decision techniques, such as, fixing the limit values of the decision variables. A cornerstone within multiobjective optimization techniques is the definition of the problem. In fact, it is necessary to specify the objective functions in an appropriate way, that is, by determining which variables compose the objective functions and the existing relations among them and the decision variables in a clear and concise way. In this case, there are two decision variables, Tmax and β, which should optimize two different objectives: i) the number of events; and ii) the performance of the system by minimizing cost function evaluation, which indirectly optimizes SOC and LOH set-point tracking and the exchange of energy with the UPG. To do that, 132 simulations have been performed considering several values of Tmax and β. In particular, it has been fixed that β∈ {10%,12%,· · · ,30%}, Tbase = 10 s, and thus, Tmax ∈ {10 s, 20 s, · · · ,120 s}. A summary of these simulations is depicted in figure 6. It shows the existing relationships between different combinations of Tmax and βparameters with the cost function evaluation (top) and the number of events (bottom). It can be seen from figure 6(top) that as Tmax and βparameters increase the performance of the system generally deteriorates quickly, and thus, better solutions for this objective are obtained for the smallest Tmax and βparameters. On the other hand, the minimum number of events is achieved with the maximum values of Tmax and βparameters while, with Tmax = 10 sand β= 1% a total number of events around 8000 has been reached. Therefore, both objectives are opposite regarding Tmax and β parameters. Hence, a set of optimal solutions has been generated from the previous graphs, see figure 7. 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Tmax (s)β(s)ISESOC ISELOH Egrid (kW h)Jeval NoEvents Computing time1(s) 30 12 9.87x1011 1.05x1012 0.6315 0.7895 8370 23.8 40 14 9.89x1011 1.04x1012 0.6349 0.9770 8048 28.4 50 16 9.94x1011 1.03x1012 0.6411 1.1613 7733 32.0 70 10 9.94x1011 1.05x1012 0.6301 0.5937 8640 22.7 80 12 9.97x1011 1.05x1012 0.6345 1.7936 8383 23.0 30 24 9.78x1011 4.91x1011 1.5870 2.8649 2880 24.3 40 26 1.01x1012 3.57x1011 1.8652 3.9649 2160 24.0 50 28 1.01x1012 2.71x1011 2.1071 4.9939 1728 30.5 Classic state-space MPC 1.301x1012 1.37x1012 0.2316 0.1286 8640 84.9 1Simulations conducted in Intel(R) Core(TM)i7-8700 CPU 3.20GHz RAM 16 GB, Windows 10x64 and Matlab R2016b 36 Table .3: Nomenclature. Acronym Meaning BCVTB Building Control Virtual TestBed Cmax Maximum energy capacity of the battery HVAC Heating, Ventilation and Air-Conditioning LOH Level of Hydrogen MPC Model Predictive Control ηConversion efficiency of each storage unit Pbat Power exchanged with the battery bank Pdem Power demanded by the office room PEM Protom Exchange Membrane Pez Power to the electrolyzer Pfc Power obtained from the fuel cell Pgrid Power exchanged with the UPG PH2Power applied to the hydrogen path Pnet Power difference between Pren and Pdem PLC Programmable Logic Controller PMV Predicted Mean Vote PRBS Pseudo-Random Binary Signal Pren Power originated by renewable energy sources SOC State Of Charge UPG Utility Power Grid Vmax Volume of H2that can be stored in the tanks ZSF1 South Zone of the First Floor 37